7.6 Modeling with trigonometric equations  (Page 3/14)

Begin by making a table of values as shown in [link] .

To model an equation, we first need to find the amplitude.

The clock’s cycle repeats every 12 hours. Thus,

The vertical shift is

There is no horizontal shift, so $C=0.$ Since the function begins with the minimum value of $y$ when $x=0$ (as opposed to the maximum value), we will use the cosine function with the negative value for $A.$ In the form $y=A\cos (Bx\pm C)+D,$ the equation is

See [link] .

As the water level varies from 7 ft to 15 ft, we can calculate the amplitude as

The cycle repeats every 12 hours; therefore, $B$ is

There is a vertical translation of $\frac{(15+8)}{2}=\mathrm{11.5.}$ Since the value of the function is at a maximum at $t=0,$ we will use the cosine function, with the positive value for $A.$

See [link] .

The period is given by

In a blood pressure function, frequency represents the number of heart beats per minute. Frequency is the reciprocal of period and is given by

See the graph in [link] .